• 12 Angry Men
• The Ladykillers
• Monsieur Hulot's Holiday
• Seven Samurai
• Wages of Fear
• Rashomon
• Invasion of the Bodysnatchers
• The African Queen
• Les Diaboliques
• Mon Oncle
• The Seventh Seal
• Forbidden Planet
• Harvey
• Singin' In The Rain

Many good movies have been mentioned here already, but I'm quite surprised that no-one yet has mentioned these:

• High Noon (1952)
• Roman Holiday (1953)
• Sabrina (1954)
• Du rififi chez les hommes (1955)
• Ice Cold in Alex (1958)
• Touch of Evil (1958)
• Vertigo (1958)
• North by Northwest (1959)

A touch of evil, that opening sequence is fantastic

The creature from the black lagoon and the incredible shrinking man are both classic 50s horror movies along with the original version of the fly, the blob, and the thing. The lost skeleton of cadavera is a pretty funny parody of the style too.

The day the earth stood still for some 50s sci-fi, and Hitchcock hits his prime in the mid to late 50s for suspense

Reviewing media I've tagged '1950s' on NeoDB & rated highly:

• Devil Girl From Mars (1954) scifi
• Les Diaboliques (1955) thriller
• Forbidden Planet (1956) scifi
• Gentlemen Prefer Blondes (1953) musical comedy
• ゴジラ Godzilla (1954) scifi
• In a Lonely Place (1950) thriller
• The Ladykillers (1955) crime comedy
• The Lavender Hill Mob (1951) crime comedy
• Singin' in the Rain (1952) musical about Hollywood itself
• I soliti ignoti (1958) crime comedy
• Stalag 17 (1953) POW drama
• 蜘蛛巣城 Throne of Blood (1957) drama & intrigue

More:

• Movies & TV tagged 1950s on NeoDB

Some I haven't seen mentioned:

• The Night of the Hunter
• Ikiru
• Paths of Glory
• Los Olvidados
• El
• The Apu Trilogy
• Sansho the Bailiff
• Nights of Cabiria

Edit: was heading out earlier. Here are some more:

• The 400 Blows
• Tokyo Story
• Wild Strawberries
• Ordet
• The Sweet Smell of Success
• Johnny Guitar
• A Man Escaped
• Pickpocket
• Hiroshima Mon Amour
• Ugetsu
• The Cranes are Flying
• The Bridge Over River Kwai
• High Noon
• Rio Bravo
• The Searchers

Bicycles Thieves (48)

From my own viewing experience, these are my recommendations that I did not see yet in the thread:

• Throne of Blood (1957)

Macbeth in feudal Japan.

• The Killing (1956)

Heist movie, early Kubrick

• The Day the Earth Stood Still (1951)

Some early sci-fi. Superior to the Keanu Reeves remake.

• Rebel Without a Cause (1955)

• Giant (1956)

A pair of James Dean roles. Unbelievable, raw talent.

• Kiss Me Deadly (1955)

Un peu de film noir.

• On the Beach (1959)

Goes well with Dr. Strangelove (1962) and Fail-Safe (1962).

Previously mentioned, and I can't help but include:

• Vertigo

• Rashomon

Edit: comments and a revision below.

• Paths of Glory (1957) — someone beat me by an hour.

The Day the Earth Stood Still

hate to beat a dead stewart but, harvey?

On the waterfront

Brando just out there setting a bar never to be surpassed

Some Like It Hot is a good one

I remember enjoying Strangers on a Train (1951).

• Zero Hour! (1957)

There's a very well known remake of this movie under a different title. Odds are that you've already seen the remake, so surely you'll find it somewhat familiar.

Casablanca